1. Field of the Invention
This invention relates to a method for determining the period of a sine wave. The invention is applicable to arrangements in which a sine wave is present in the form of discrete samples, as distinct from a complete continuous wave. The invention is particularly, but not exclusively, applicable to systems for determining the distance to an object using a frequency-modulated carrier combined with pulse transmission such that the distance is determined by the beat frequency derived by combining transmitted and object-reflected signals. Such systems, which may for example have microwave sensors to detect obstacles, could be used as automotive radar systems.
2. Description of the Prior Art
One of many systems, such as those described in WO 03/044559 A1, WO 03/044560 A1, U.S. Pat. No. 6,646,587 B2, JP 2000275333, JP2004333269 and JP2004144696, employed for automotive warning and collision avoidance is frequency modulated interrupted continuous wave (FMICW) radar. In such a system, shown in a block form in FIG. 1, the frequency of a carrier generated by an oscillator OSC is linearly swept in a periodic fashion with a period TSW over a predetermined frequency range ΔF using a frequency modulator FM in a voltage controlled oscillator VCO. A modulation pattern is provided by a linear waveform generator LWG under the control of a control module CM. The frequency modulated continuous wave (FM-CW) signal is coupled by a coupler CPL to a power amplifier PA where it is amplified, and then gated by means of a transmit-receive switch TRS triggered by the control module CM and operating at a pulse repetition frequency PRI. The transmit-receive switch TRS periodically couples the output of power amplifier PA to an antenna AN for a short interval ΔTT to obtain a pulsed RF transmission signal TX directed towards an obstacle OB of interest. During this interval, which is usually a small fraction of a gating period TPRI=1/PRI, the switch TRS keeps the radar receiver disconnected from the antenna. The reflected signal RX, delayed by a time τ proportional to the object distance D, is detected by the same antenna and coupled to a low-noise amplifier LNA via the transmit-receive switch TRS.
The pulse signal reflected from the obstacle is mixed in a downconverter DR with a reference signal formed by a version of the transmitted signal received from the coupler CPL. Because the transmitted and received pulsed signals are mutually delayed, the instantaneous frequencies of the transmitted and received pulsed signal are different. Therefore, the beat signal obtained at the output of downconverter has a differential frequency FD, which is directly proportional to the unknown distance D to the obstacle.
The output of the downconverter DR is delivered to a signal processor module SPM, which comprises an analogue-to-digital converter ADC and a digital processor DP driven by clock pulses from a clock CLK. The converter ADC converts the signal s(t) from the downconverter DR into a digital signal used by the digital processor DP to determine the beat frequency and hence object range.
The modulation pattern provided by the linear waveform generator LWG may follow, for example, a periodical triangular waveform with a constant slope, as shown in FIG. 2a. Employing this particular waveform is often preferred to other linear modulation schemes (such as sawtooth) since it also allows estimation of the velocity of moving obstacles from the Doppler frequency calculated from a pair of differential frequency shifts derived from transmitted and received signals at rising and falling parts of the triangular waveform.
FIG. 2b shows pulsed signals observed at various points of the system of FIG. 1. It can be seen that the operation of switch TRS ensures that the reflected signal is coupled to the radar receiver only during predetermined time slots ΔTR, which are outside time slots ΔTT used for sending the signal from the transmitter. Such a gating scheme minimises strong signals originating from antenna coupling, which can lead to unwanted effects in the receiver such as saturation of the receiver amplifier and/or the analogue-to-digital converter ADC.
In FMICW radar, accurate results are more difficult to obtain with short object distances. Short distances give rise to beat signals having a period TD=1/FD which is relatively long. If the distance is sufficiently short, the period is greater than the duration TSW of the frequency sweep. Such a particular case is presented in FIG. 2c. This causes difficulties in estimating the beat frequency, particularly if, as in prior art systems, the envelope, and thus the frequency FD of the signal, is estimated from the received train of pulses observed during a single frequency sweep of duration TSW.
Another limitation of short distance performance of FMICW radar results from the above-described gating scheme performed by the switch TRS. As is shown in FIG. 2b, for time-delays τ shorter than duration ΔTT of transmitted pulses, the duration ΔTDR (and hence the energy) of the pulses delivered to the downconverter DR is reduced. The shape of such shortened pulses is more likely to be distorted due to, for example, noise and bandwidth limitations in the amplifier LNA and the downconverter DR. As a result, the sampling process performed in the converter ADC at the rate governed by a clock CLK may not correctly determine the amplitude of the pulse. This may lead to errors in estimating the beat frequency from calculations performed in a digital processor DP, and thus a wrong indication regarding obstacle distance.
Further problems associated with short object distances can be seen from the following example.
Assume that an automotive FMICW radar has the following parameters:                duration TSW of a linear frequency sweep, TSW=4 ms;        frequency excursion AF during the sweep, ΔF=80 MHz;        pulse repetition interval TPRI=2 μs        
FIG. 2a depicts schematically the relationship between time and frequency, the frequency/time characteristic, for the notional automotive radar under analysis.
Because, in this case, the pulse repetition interval TPRI is equal to 2 μs, the unambiguous range of distance measurement will extend to 300 m. In a radar employing a linear frequency sweep, the distance D to an obstacle is determined from the difference FD between two frequencies: the frequency of a transmitted signal and that of a signal reflected by the obstacle, where
                              F          D                =                                            2              ⁢              D                        c                    ⁢                      S            FT                                              (        1        )            where c is the speed of light and SFT is the slope of the frequency/time characteristic, given by
                              S          FT                =                                            Δ              ⁢                                                          ⁢              F                                      T              SW                                =                      20            [                          Hz              ns                        ]                                              (        2        )            
Therefore, in the considered case, an obstacle at a distance D=3 m will give rise to a differential (beat) frequency FD of 400 Hz.
If the measurement of beat frequency FD (hence, distance determination) is to be accomplished using samples acquired within the time interval equal to the duration TSW of a frequency sweep, then the width of the frequency step (bid) of spectral analysis is equal to 1/Tsw=250 Hz. The 3-dB bandwidth and the support of the main lobe are equal to 0.9/Tsw and 2/Tsw, respectively.
As well known to those skilled in the art, this 3-dB bandwidth will increase when a suitably shaped observation window of duration Tse, is applied to a received signal to suppress undesired frequency sidelobes. For example, for a Hamming window, the 3-dB bandwidth of the main lobe will be equal to 1.3/TSW.
FIG. 4 illustrates the effects of finite observation time in the process of frequency and distance determination. As seen, the relative error in distance measurement increases at shorter distances, leading to a significant performance degradation.
From the above it follows that FMICW radar systems exploiting the described signal-processing scheme would suffer from performance loss at short distances. It would therefore be desirable to develop a novel signal-processing method and an apparatus for improving the performance of FMICW radar particularly at short ranges in a more efficient way than provided by prior art techniques, especially in applications for collision avoidance or/and warning systems.
There are two well-known time-domain period/frequency estimators suitable for extracting information from short segments of a sine wave with unknown amplitude A, period T and initial phase θ. The duration of a segment under analysis may be as short as a single period of a sine wave, or even shorter.
The two estimators are:
Zero-crossing estimator
Slope/amplitude estimator
The principles of these two time-domain estimators are illustrated in FIGS. 5a and 5b, respectively.
In the zero-crossing estimator, the signal s(t)=A sin(2πt/T+θ) is converted, explicitly or implicitly, into a binary representation b(t)=sign[s(t)] so that the times t1 and t2 at which the level of the sine wave successively crosses zero are determined. The unknown period {circumflex over (T)} is estimated from the following equation{circumflex over (T)}ZC=2(t2−t1)  (3)
In the slope-amplitude estimator, the times t1 and t2 are again determined. The rising and falling slopes S+ and S− of the sine wave at each of these two instants are also determined. The unknown period T is estimated from
                                          T            ^                    SA                =                              2            ⁢            π            ⁢                                                  ⁢            A                                            S                                                          (        4        )            where the amplitude A is estimated as max|s(t)| or |s[(t2−t1)/2]|, and slope |S| is the average of the slopes |S+| and |S−|.
However, it would be desirable to have a technique, preferably suited for FMICW radar, which is more efficient, and more accurate, than each of these two conventional time-domain estimators. It would also be desirable to provide a technique which measures a sine wave period using samples of the sine wave and which works well even when the samples are shortened as described above.